Ab initio calculations, also known as first-principles calculations, are computational methods used to predict the electronic structure and properties of molecules and materials based on the fundamental principles of quantum mechanics. These calculations can be employed to study the excited state dynamics of a molecule and identify the potential energy surfaces PES involved in the relaxation of the excited state back to the ground state. Here's a step-by-step approach to achieve this:1. Choose an appropriate level of theory: Select a suitable quantum mechanical method, such as time-dependent density functional theory TD-DFT , complete active space self-consistent field CASSCF , or multi-reference configuration interaction MRCI , depending on the size of the molecule and the complexity of the excited states.2. Perform geometry optimization: Optimize the molecular geometry of the ground state and the excited states using the chosen level of theory. This will provide the equilibrium geometries and energies of the ground and excited states.3. Calculate excited state energies and transition properties: Perform ab initio calculations to obtain the vertical excitation energies, oscillator strengths, and transition dipole moments for the excited states. This information will help in understanding the nature of the excited states and their possible relaxation pathways.4. Construct potential energy surfaces: Based on the calculated excited state energies and geometries, construct the potential energy surfaces for the ground and excited states. These surfaces represent the energy landscape of the molecule as a function of its nuclear coordinates and can be used to study the relaxation dynamics.5. Identify conical intersections and minimum energy crossing points: Analyze the potential energy surfaces to identify conical intersections where two or more PESs intersect and minimum energy crossing points MECPs, where the energy difference between two PESs is minimum . These regions are critical for non-adiabatic transitions between different electronic states and play a significant role in the relaxation of the excited state.6. Perform excited state molecular dynamics simulations: Carry out non-adiabatic molecular dynamics simulations on the potential energy surfaces to study the relaxation dynamics of the excited state. These simulations will provide insights into the time evolution of the excited state population and the pathways for relaxation back to the ground state.7. Analyze the results: Analyze the results of the molecular dynamics simulations to identify the dominant relaxation pathways and the role of conical intersections and MECPs in the relaxation process. This information can be used to understand the excited state dynamics and design strategies to control the relaxation process in the molecule.By following these steps, ab initio calculations can be used to predict the excited state dynamics of a molecule and identify the potential energy surfaces involved in the relaxation of the excited state back to the ground state.